# Derivative of a Reciprocal

How to find the derivative of a reciprocal 1/g(x): formula (reciprocal rule), 1 example, and its solution.

## FormulaReciprocal Rule

The derivative of 1/g(x) is -g'(x)/[g(x)]^{2}.

## Exampley = 1/(x^{3} + 2x), y' = ?

Solution

Solution (Detail)

1/(x^{3} + 2x) is the reciprocal of (x^{3} + 2x).

So y' is equal to ...

Write - and the fraction bar.

Write, the derivative of (x^{3} + 2x), 3x^{2} + 2

in the numerator.

Derivative of a Polynomial

Write, the square of (x^{3} + 2x), (x^{3} + 2x)^{2}

in the denominator.

So

y' = -(3x^{2} + 2)/(x^{3} + 2x)^{2}

is the derivative of the function.